Today’s my mummy’s birthday. I want to make a birthday cake for her. It should contain exactly m cylinder-shaped layers, and its volume should be exactly nπ. We number the cylinders 1, 2, . . . , m from bottom to top. The i-th cylinder has a positive integer radius ri and a positive integer height hi. To make the cake look pretty, It should be satisfied that for all i < m,ri > ri+1 and hi > hi+1. The surface of the cake will be entirely ice cream. To make the cake a little bit cheaper, we decide to use as little ice cream as possible. In other words, the surface area (excluding the bottom surface, since there is no ice cream on the bottom of course) should be minimized. Input The input consists of at most 10 test cases. Each case contains two integers n, m (n < 100001, m < 11), the volume and the number of layers of the cake. The last case is followed by a single zero, wich should not be processed. Output For each test case, print the case number and an integer S, where Sπ is the minimal surface area. If the cake cannot be made, print a single zero. Sample Input 100 2 1000 3 0 Sample Output Case 1: 68 Case 2: 316